I feel that 22ga stranded is about the best type of wire you can use on cabinets. It's thin enough so even when it's bundled together, it is still pliable and easy to maneuver around in your cabinet, yet still thick enough to fit nicely in red disconnects without any trouble.
The key to keeping everything neat when using single strands is to use
lots of nylon zip ties. I normally zip tie wires together on about 4" centers, and that keeps all the wires cleanly bunched together. I can easily use up a 100 pack of zip ties in just one cabinet, but I might take it to extremes, too. You can probably save yourself the time of rewiring everything by just going back and bundling the wires together, providing that you left enough slack in the wires to let you do this.
I even go back and zip tie the multi-conductor cables together, too, but that may be overkill. The other thing I do is use a staple gun and make a path where the wires are going to go, leaving the staple heads protrude about 1/8" - 3/16", then zip tie the wire bundles to the staples. If you look closely at this pic, you can just barely make out the staples where the wires are attached to the sides of the cabinet.
http://www.oscarcontrols.com/cocktail/wiring8.jpg##EDIT##
BTW -
Here is the multi-conductor cable I use on my projects for those that are interested. 400' of wire for $18 isn't that bad and goes a long way to make your wiring nice and neat!